Light modulation can be programmably controlled by electrical signals and has been widely used in data processing devices and communication systems (e.g., cable TV). One implementation of programmable light modulation is electro-optic ("EO") light modulation by using an electro-optic material (e.g., crystals) whose index of refraction changes in response to an externally applied electrical field.
Traveling-wave EO modulators are suitable for light modulation at high frequencies such as in a range above .about.10.sup.8 Hz. Light modulation using traveling-wave modulators is known to the art. See, for example, "Optical Waves in Crystals: propagation and Control of Laser Radiation", by Yariv and Yeh, John Wiley and Sons (1980). In a traveling-wave EO modulator, the direction of the electrical field of a modulating field is usually perpendicular to the propagation direction of the optical wave. In particular, the modulating wave travels along with the optical wave in substantially the same propagation direction. Much effort in research and development has been made in designing traveling-wave modulators due to their applications in data processing and communication devices and systems. Compact integrated EO modulators are of particular interest in this field for optical fiber networks and other applications.
FIG. 1 shows a conventional traveling-wave light modulator 100. An EO material 102 of length L with optical input and output facets 104 and 106 is placed between two parallel electrodes 110 and 112. In an integrated modulator configuration, the EO material 102 forms a substrate on which an optical waveguide and the electrodes are formed. A modulation signal source 114 is connected to the electrodes 110 and 112 at their ends near the input facet 104 to launch a traveling modulation wave at a modulation frequency .omega..sub.mod. A signal terminator 116 with a load can be used to terminate the modulating waves at the other ends of the electrodes 110 and 112 close to the output facet 106 of the EO material 102. If the phase velocities of the optical and modulating waves are equal to each other, a portion of an optical wavefront of the optical wave experiences the same instantaneous modulating electrical field. This corresponds to the field which that portion of the optical wavefront encounters at the input facet 104. Such a match in the phase velocities is desirable since the efficiency of modulation is maximum as described hereinafter.
However, material dispersion often adversely affects or prevents this desired phase match condition. Phase velocities of electrical and optical waves are different in most cases. The electrical modulation wave travels at a phase velocity .upsilon..sub.mod usually lower than the phase velocity .upsilon..sub.opt of the optical wave. In an integrated modulator, this mismatch in phase velocities is primarily caused by the dispersion of the electro-optic material of the substrate. The modulation wave and the optical wave then experience different indices of refraction due to their different frequencies. This can limit the EO modulator to operate at higher modulation frequencies and significantly reduce the modulation depth.
The phase modulation depth .delta. of the traveling-wave modulator 100 can be approximately expressed as ##EQU1## where .beta. is a factor linearly proportional to the magnitude of the electrical field of the modulation wave and the electro-optic coefficient of the crystal and .DELTA. is a phase mismatch parameter: ##EQU2## The phase modulation depth .delta. increases proportionally with the interaction length L. In addition, the phase modulation depth .delta. is dependent on a phase mismatch parameter .DELTA. and reaches at or near a maximum value when .DELTA.=0, i.e., the phase velocities .upsilon..sub.mod and .upsilon..sub.opt are equal to each other. Otherwise, the phase modulation is reduced by a factor due to the phase mismatch between the optical wave and the electrical modulation wave. An ideal phase match requires .upsilon..sub.mod =.upsilon..sub.opt. This is usually difficult to achieve in practical devices. In practice, the phase match condition may be considered satisfactory if EQU .omega..sub.mod .DELTA.L&lt;&lt;.PI.. (3)
Another parameter which sets the performance of the EO modulators is the sensitivity of modulation. It is desirable to achieve a maximal phase modulation depth .delta. with a smallest possible drive signal power for a given electro-optic material. This can be accomplished, for example, by increasing the interaction length L of the electro-optic material while maintaining the phase match condition in Equation (3). In addition, choosing an electro-optic material with a large electro-optic coefficient can reduce the drive power required for the modulator.
The phase match condition of the optical wave and the electrical modulation wave can be achieved by implementing a traveling-wave configuration in an EO modulator. In general, this can be done by either reducing the phase velocity of the optical wave or speeding up the electrical wave. One way to accomplish the former is disposing bends with a higher refractive index in the waveguide. However, loss by light scattering in the bends is often unacceptably high, thus making this technique impractical in many applications.
There have been two different approaches in increasing the effective phase velocity of the electrical wave to match that of the optical wave.
One approach utilizes a buffering layer of a low index insulator, such as a SiO.sub.2 layer, between the electro-optic crystal and an electrode wherein the electrical wave propagates. See, Gopalakrisna et al., "40 GHZ Low Half Wave Voltage Ti:LiNbO3 Intensity Modulators", Electronic Letters, Vol. 28, pp. 2056-2068 (1995). This buffering layer lifts the fields out of the crystal and effectively reduces the index of refraction experienced by the electrical wave. As a result, the phase velocity of the electrical wave is increased. This velocity matching technique can be effective. However, field penetration to the crystal is reduced and consequently the modulation sensitivity is compromised. Another limitation of this approach is that a large and uniform buffering layer is usually difficult to grow and can be expensive.
A second alternative approach is to increase the speed of the electrical wave on the average rather than uniformly in the electrical path. Therefore, the phase velocity of an electrical wave may not have been equal to the optical phase velocity. However, on the average, the phase mismatch between the electrical wave and the optical wave is minimized. One implementation of this approach uses a plurality of small and separate electrodes to form an electrode array along each side of the optical path (e.g., the optical waveguide in an integrated system) instead of having a single-piece electrode on each side of the optical path in the electro-optic material. The modulator splits the electrical modulation wave accordingly into a plurality of portions with each being fed to one of the small electrodes. Multiple electrical paths from the modulation signal source to each small electrode are formed in a way such that the initial phase of each portion of the input electrical modulation wave at a corresponding small electrode matches the phase of the optical wave. A small phase mismatch develops as each portion of the electrical wave propagates along each small electrode. However, the average phase mismatch for the entire electrode array is substantially eliminated. This is because, at least in part, the length of each small electrode is small compared to the interaction length.
U. S. Pat. No. 5,076,655 to Bridges describes such a system which uses an antenna array to implement the electrode array. An electrical modulation wave is used to illuminate the antenna array at a selected angle with respect to the array so that a modulation electrical wave arriving at each antenna has a different phase delay and matches the phase of the optical wave at that antenna. U.S. Pat. No. 5,291,565 to Schaffner et al. discloses another system to implement the above technique.
This second approach for speeding up the electrical wave may also be limited in several respects. For example, splitting the electrical modulation wave into multiple waves (e.g., N waves) reduces the voltage on each electrode in the array by a factor of N.sup.1/2, thereby decreasing the modulation sensitivity. In addition, the structure of the RF electrode array is complex and accordingly the construction of the entire modulator becomes complicated.